Abstract
The nonlinear nth‐order differential equations are considered. By using inequality techniques and coincidence degree theory, some criteria are obtained to guarantee the existence and uniqueness of T‐periodic solutions for the equations. The obtained results are also valid and new for the problem discussed in the previous literature. Moreover, two illustrative examples are provided to illustrate the effectiveness of our results.
Highlights
In applied science, some practical problems are associated with the periodic solutions for nonlinear high-order differential equations, such as nonlinear oscillations 1, 2, electronic theory 3, biological model, and other models 4–6
The purpose of this paper is to investigate the existence and uniqueness of T periodic solutions of 1.1
By the same approach used in the proof of Lemma 3 of 7, we have the following
Summary
Some practical problems are associated with the periodic solutions for nonlinear high-order differential equations, such as nonlinear oscillations 1, 2 , electronic theory 3 , biological model, and other models 4–6. Under some spectral conditions of linear differential operator, Li 12, 13 discussed the existence and uniqueness of T -periodic solutions of nonlinear differential equations. To the best of our knowledge, there exist few results for the existence and uniqueness of periodic solutions of 1.1 without H and the spectral conditions of linear differential operator. In this case, it is worth to study the problem of existence and uniqueness of periodic solutions of nth-order nonlinear differential equation 1.1.
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